A journey down the rabbit hole of Rubik's-style puzzles

In my last post, I wrote about new custom stickers from Olivér Nagy. Besides some great new custom logo stickers, he and I worked on a sticker template for Rubik’s-brand Void Cubes. The OEM Void stickers have a ridiculous pattern of concentric circles and the color scheme is a bit funky — with white replaced by red and red replaced by a magenta-purple. Re‑stickering to a familiar color scheme made it a lot easier to solve!

As long as I had the camera rolling, I decided to do a quick walk-through video. A lot of folks think the Void Cube is some alien beast when it comes to solves. In reality, with one key parity exception, it solves just like a 3×3. The video walks through that parity issue, which is more fully explained after the jump.

The potential PLL parity issue on a Void Cube results from the “centers” being swapped in a way that could not happen on a 3×3. Of course, the Void Cube doesn’t have centers as such. But if the scramble + solve leaves the would-be centers — imagine that the centers were there since the last solved state — in an odd state, so to speak, the puzzle is said colloquially to have parity or a parity error.

This is parallel to parity on a 4×4, which I break down in detail (math/puzzle theory, probabilities, etc.) in this post. The Void parity becomes evident when, at the PLL stage, the case is one that could not occur on a 3×3. It is corrected by aplying an algorithm that switches the odd state to an even state, such as this one:

M’ U2 (M U M U) (M’ U’ M’)

In configuring the “centers,” the algorithm also will jumble some of the top edges, requiring re-doing OLL. But, once the OLL is complete, the PLL will be one of the 21 cases that can occur on a 3×3.